A new topological classification of points in 3D images
We propose, in this paper, a new topological classification of points in 3D images. This classification is based on two connected components numbers computed on the neighborhood of the points. These numbers allow to classify a point as an interior or isolated, border, curve, surface point or as different kinds of junctions.
The main result is that the new border point type corresponds exactly to a simple point. This allows the detection of simple points in a 3D image by counting only connected components in a neighborhood. Furthermore other types of points are better characterized.
This classification allows to extract features in a 3D image. For example, the different kinds of junction points may be used for characterizing a 3D object. An example of such an approach for the analysis of medical images is presented.
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- 1.T.Y. Kong and A. Rogenfeld. Digital topology: introduction and survey. Computer Vision, Graphics and Image Processing, 48:357–393, 1989.Google Scholar
- 2.V.A. Kovalevsky. Finite topology as applied to image analysis. Computer Vision, Graphics, And Image Processing, 46:141–161, 1989.Google Scholar
- 3.G. Malandain and G. Bettrand. A new topological segmentation of discrete surfaces. Technical report, I.N.R.I.A., Rocquencourt, 78153 Le Chesnay Cédex, France, 1992.Google Scholar
- 4.G. Malandain, G. Bertrand, and N. Ayache. Topological segmentation of discrete surfaces. In IEEE Computer Vision and Pattern Recognition, June 3–6 1991. Hawaii.Google Scholar
- 5.O. Monga, N. Ayache, and Sander P. From voxel to curvature. In IEEE Computer Vision and Pattern Recognition, June 3–6 1991. Hawaii.Google Scholar
- 6.O. Monga, R. Deriche, G. Malandain, and J.P Cocquerez. Recursive filtering and edge closing: two primary tools for 3d edge detection. In First European Conference on Computer Vision (ECCV), April 1990, Nice, France, 1990. also Research Report INRIA 1103.Google Scholar
- 7.D.G. Morgenthaler. Three-dimensional digital topology: the genus. Tr-980, Computer Science Center, University of Maryland, College Park, MD 20742, U.S.A., November 1980.Google Scholar
- 8.C.M. Park and A. Rosenfeld. Connectivity and genus in three dimensions. Tr-156, Computer Science Center, University of Maryland, College Park, MD 20742, U.S.A., May 1971.Google Scholar